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27^2/3
<-- Enter Number or variable Raised to a fractional power such as a^b/c
Term 1
Simplify the rational exponent
27
^{2/3}
Analyze Fractional Exponent:
The rule of fractional exponents states that a
^{b/c}
is evaluated as follows:
a
^{b/c}
= (
^{c}
√
a
)
^{b}
That is equivalent to saying we take the c
^{th}
root of a, and then raise that value to the power of b
In this case, a =
27
, b =
2
, and c =
3
Evaluate the
3
^{rd}
root of
27
:
^{3}
√
27
= 3 since 3
^{3}
= 27
as seen in our Exponent Lesson
Raise this value to the power of
2
:
Therefore, we can write
27
^{2/3}
=
9